How many seconds after it was hit did the ball hit the ground, to the nearest second?

Question

The following function gives the height, h metres, of a batted baseball as a function of the time, t seconds, since the ball was hit.

 

h = -6(t-2.5)^2 + 38.5 

Answer 1

h(t) = -6(t - 2.5)^2 + 38.5;  assume that h(t) is measured from ground level, in which case (incidentally) 

 

h(0) = -6(2.5^2) + 38.5 = 38.5 - 6(6.25) = 38.5 - 36 - 1.5 = 1;  then, h(T) = 0, when ball hits ground;

 

or,  -6(T - 2.5)^2 +38.5 = 0  ---> (T - 2.5)^2 = 38.5/6 ---> T - 2.5 = sqrt(38.5/6) ---> T = 2.5 + sqrt(38.5/6)

 

note:  we can ignore the "-" when taking square roots, as this would imply that T < 0, which would not be appropriate

          in the context of this problem.